The modulus of elasticity (MOE) is a measure of stiffness.
For MDF it's 0.53, for particle board it's 0.7, for fir plywood it's 1.2
so plywood is definitely stiffer.
Sub floor bracing is provided to transfer sideways loads down to the ground.
Bracing needs to be provided at all levels to work. Imagine a building in a wind that had bracing to resist the wind at the roof and wall levels, but not at the sub floor level.